• SJSU Singular Matrix Database
  • Matrix group: GHS_indef
  • Click here for a description of the GHS_indef group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups

  • Matrix: GHS_indef/ncvxqp1
  • Description: Gould, Hu, & Scott: KKT matrix - nonconvex QP (CUTEr)
  • download as a MATLAB mat-file, file size: 323 KB. Use SJget(481) or SJget('GHS_indef/ncvxqp1') in MATLAB.
  • download in Matrix Market format, file size: 256 KB.
  • download in Rutherford/Boeing format, file size: 259 KB.


    A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

    Routine svds_err, version 1.0, used with Matlab (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0 with opts.tol_eigs = 1e-008, used with Matlab (R2008a) to calculate singular values 7085 to 7090 and associated error bounds.


    Matrix properties (click for a legend)  
    number of rows12,111
    number of columns12,111
    structural full rank?yes
    structural rank12,111
    numerical rank 7,087
    dimension of the numerical null space5,024
    numerical rank / min(size(A))0.58517
    Euclidean norm of A 7.5802e+012
    calculated singular value # 708712.93
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 70887.4116
    gap in the singular values at the numerical rank:
    singular value # 7087 / singular value # 7088
    calculated condition number-2
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorN. Gould
    editorN. Gould
    kindoptimization problem
    2D/3D problem?no

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))2,222,105 1,280,499
    Cholesky flop count2.2e+009 6.2e+008
    nnz(L+U), no partial pivoting4,432,099 2,548,887
    nnz(V) for QR, upper bound nnz(L) for LU6,506,571 2,972,102
    nnz(R) for QR, upper bound nnz(U) for LU14,173,093 6,554,101

    Maintained by Leslie Foster, last updated 24-Apr-2009.

    Entries 5 through 14 in the table of matrix properties and the singular
    value plot were created using SJsingular code. The other plots
    and statistics are produced using utilities from the SuiteSparse package.
    Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.